Ultimate Intelligence Part I: Physical Completeness and Objectivity of Induction

TL;DR

This paper argues that Solomonoff induction is physically complete and applicable to quantum mechanics, proposing a physical basis for universal induction and addressing objections through new complexity measures.

Contribution

It introduces a physical framework for Solomonoff induction, including defining physical message complexity and probability, and explores variants based on energy and action.

Findings

Solomonoff induction is physically complete.

A physical reference machine for universal induction is proposed.

Variants of physical message complexity are introduced.

Abstract

We propose that Solomonoff induction is complete in the physical sense via several strong physical arguments. We also argue that Solomonoff induction is fully applicable to quantum mechanics. We show how to choose an objective reference machine for universal induction by defining a physical message complexity and physical message probability, and argue that this choice dissolves some well-known objections to universal induction. We also introduce many more variants of physical message complexity based on energy and action, and discuss the ramifications of our proposals.